In a known arrangement of this kind (EP-A2-0 153 298), the aim is to detect precisely the variation of the welding parameter in time and to define precisely a desired run of data associated with a welding operation, in the course of which various marginal conditions, particularly the kind of material, the thickness of material, a coating of the material, the basic parameter of the particular welding machine etc., are to be taken into consideration and the data obtained are to be combined and evaluated in accordance with various programs. For this purpose, in the known arrangement, a favorable course of the welding parameter is determined for each individual welding position on a sample workpiece having a plurality of welding positions, and is stored. The store can be programmed through a microprocessor so that it is possible to select a welding pattern w is recognized as being particularly favorable and also store its data profile as a desired profile for following like welding operations. Then, when the welding machine is in series operation, the associated reference data for the particular welding position, are retained as a desired profile in the store, and recalled. As a result of interrogating the instantaneous values of the welding parameter during the welding operation, a data profile result is compared, in a comparator, with the stored data profile corresponding to the desired course of the welding operation. Output signals are generated according to the degree of agreement found. If a minimum degree of agreement is found, the weld can be evaluated as "good". It is not stated, however, how the limiting value for the minimum degree of agreement between desired and actual course, for which the weld can be evaluated as "good" is set. It is to be assumed that a fixed value is set which is at a certain margin from the desired course. In order that the set limiting value may be able to be used for the whole length of the weld seam, without too many satisfactory welds being rejected as "poor", a relatively large set limiting value must be selected. Otherwise, great deviations usually occurring at the beginning and end of the weld seam would continuously lead to erroneous rejects. The known device is therefore not very sensitive and not very precise in quality control.